Chemistry Reference
In-Depth Information
where
V
1
o
is the partial molecular volume of the pure solvent,
V
1
o
= ρ
-1
; κ
T
is the
corresponding solvent isothermal compressibility; and the partial molecular vol-
ume of the salt at infinite dilution
V
2
∞
provides the link to the system structure
through the total correlation function integrals (TCFI) as follows (Kusalik and
Patey 1987; Chialvo et al. 1999),
(
)
∞
o
o
∞
V
=
ν
V
+
GG
−
(8.2)
2
1
11
12
where
G
1
o
and
G
1
∞
are the TCFI for the solvent-solvent and solute-solvent interac-
tions, respectively.
Because
V
2
∞
comprises a solvation contribution (associated with the solvent's
local density perturbation) and a compressibility-driven contribution (associated
with the propagation of the perturbation), it also offers a way to identify the short-
and long-ranged contributions to this mechanical partial molecular property, and
consequently, to discriminate the solvation process from the compressibility-driven
phenomenon. In fact, after invoking the Ornstein-Zernike equation (Hansen and
McDonald 1986), we can split the TCFIs into their direct and indirect contributions
(Chialvo et al. 1999), that is,
(
)
+
(
)
∞
o
o
∞
o
∞
VVCC
=
ν
1
+
−
ν
I
−
I
(8.3)
2
1
11
12
11
12
where
I
ij
=
G
ij
- ρ
-1
C
ij
represents the integral over the indirect pair correlation func-
tions (ICFIs), for the
ij
-interactions (Chialvo and Cummings 1994). Then, it becomes
clear that the first term in Equation 8.3 represents the solvation (finite) contribution
to
V
2
∞
,
V
2
∞
(SR), that is
,
(
)
∞
o
o
∞
V
()
SR
=
ν
V
1
+
CC
−
(8.4)
2
1
11
12
while the second term accounts for the compressibility-driven contribution,
V
2
∞
(LR),
that is, (Chialvo et al. 1999)
(
)
VLRk TCCC
BT
∞
()νκ
o
=
o
−
∞
(8.5)
2
11 1
12
where
C
1
o
and
C
1
∞
are the direct correlation function integrals (DCFIs) for the solvent-
solvent and solute-solvent interactions, respectively (Kusalik and Patey 1987;
O'Connell 1990).
The concept of short- and long-ranged contributions highlights the fact that the
invoked correlation function integrals are either finite (DCFI) or diverging (ICFI)
quantities, the result of volume integrals over either short- (direct) or long-ranged (indi-
rect) correlation functions. Note also that both quantities involve the same finite factor
C
1
o
-
C
1
∞
linked to the solute-solvent molecular asymmetry, whose actual meaning can
be revealed in a few insightful alternative representations of the structural perturbation
of the solvent caused by the mutation of a solvent into the solute during the
thought
